Relations and Functions

If $A = {1, 2, 3}$ and $B = {3, 4}$, then $(A \cup B) \times (A \cap B)$ is:

If $P = {1, 2}$, form the set $P \times P \times P$.

If $A \times B = {(a, x), (a, y), (b, x), (b, y)}$, find $A$ and $B$.

Let $A = {1, 2}$ and $B = {3, 4}$. The number of relations from $A$ to $B$ is:

Let $R$ be the relation on $\mathbb{N}$ defined by $R = {(x, y) : y = x + 5, x < 4, x \in \mathbb{N}}$. The domain of $R$ is:

Let $A = {1, 2, 3, ..., 14}$. Define a relation $R$ from $A$ to $A$ by $R = {(x, y) : 3x - y = 0$, where $x, y \in A}$. The range of $R$ is:

Let $R$ be a relation on the set $\mathbb{R}$ of real numbers defined by $R = {(a, b) : a \le b^2}$. Is $R$ reflexive?

The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = 2x$ is:

The function $f: \mathbb{N} \to \mathbb{N}$ defined by $f(x) = x^2$ is:

The domain of the real function $f(x) = \frac{1}{\sqrt{x^2 - 4}}$ is:

The range of the real function $f(x) = |x|$ is:

Let $f(x) = x^2$ and $g(x) = 2x + 1$ be two real functions. Then $(f + g)(x)$ is:

If $f(x) = x^3$, then the value of $\frac{f(3) - f(1)}{3 - 1}$ is:

The domain of the signum function $sgn(x) = \begin{cases} 1, & x > 0 \ 0, & x = 0 \ -1, & x < 0 \end{cases}$ is:

The range of the signum function $sgn(x)$ is:

If $n(A) = 3$ and $n(B) = 2$, then the number of elements in $A \times B$ is:

The greatest integer function $f(x) = [x]$, which floors $x$ to the greatest integer less than or equal to $x$, has the domain:

The range of the greatest integer function $f(x) = [x]$ is:

If $f(x) = \frac{x-1}{x+1}$, then $f(-1)$ is:

Let $A = {1, 2, 3}$. The total number of reflexive relations on set $A$ is not directly asked, but consider a relation $R$ on $A$ containing $(1,1), (2,2), (3,3)$. What kind of relation is this?

If $f(x) = x^2 - 3x + 2$, find $f(f(0)).$